JP Journal of Algebra, Number Theory and Applications
-->
Abstract: Let R
be a commutative ring. A full additive subcategory of R-modules is triangulated if whenever two terms of a short
triangulated sequence belong to then so does the
third term. In this note, we give a classification of triangulated subcategories
of finitely generated modules over a principal ideal domain. As a corollary, we
show that in the category of finitely generated modules over a PID, thick
subcategories (triangulated subcategories closed under direct summands), wide
subcategories (abelian subcategories closed under extensions) and Serre
subcategories (wide subcategories closed under kernels) coincide and correspond
to specialisation closed subsets of Spec (R).
Keywords and phrases: triangulated subcategory, abelian subcategories, principal ideal domains.
